© 2021, CERN for the benefit of the CMS collaboration.This paper presents new sets of parameters (“tunes”) for the underlying-event model of the HERWIG7 event generator. These parameters control the description of multiple-parton interactions (MPI) and colour reconnection in HERWIG7, and are obtained from a fit to minimum-bias data collected by the CMS experiment at s=0.9, 7, and 13Te. The tunes are based on the NNPDF 3.1 next-to-next-to-leading-order parton distribution function (PDF) set for the parton shower, and either a leading-order or next-to-next-to-leading-order PDF set for the simulation of MPI and the beam remnants. Predictions utilizing the tunes are produced for event shape observables in electron-positron collisions, and for minimum-bias, inclusive jet, top quark pair, and Z and W boson events in proton-proton collisions, and are compared with data. Each of the new tunes describes the data at a reasonable level, and the tunes using a leading-order PDF for the simulation of MPI provide the best description of the data.